{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<!--BOOK_INFORMATION-->\n",
    "<a href=\"https://www.packtpub.com/big-data-and-business-intelligence/machine-learning-opencv\" target=\"_blank\"><img align=\"left\" src=\"data/cover.jpg\" style=\"width: 76px; height: 100px; background: white; padding: 1px; border: 1px solid black; margin-right:10px;\"></a>\n",
    "*This notebook contains an excerpt from the book [Machine Learning for OpenCV](https://www.packtpub.com/big-data-and-business-intelligence/machine-learning-opencv) by Michael Beyeler.\n",
    "The code is released under the [MIT license](https://opensource.org/licenses/MIT),\n",
    "and is available on [GitHub](https://github.com/mbeyeler/opencv-machine-learning).*\n",
    "\n",
    "*Note that this excerpt contains only the raw code - the book is rich with additional explanations and illustrations.\n",
    "If you find this content useful, please consider supporting the work by\n",
    "[buying the book](https://www.packtpub.com/big-data-and-business-intelligence/machine-learning-opencv)!*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<!--NAVIGATION-->\n",
    "< [Implementing a Spam Filter with Bayesian Learning](07.00-Implementing-a-Spam-Filter-with-Bayesian-Learning.ipynb) | [Contents](../README.md) | [Classifying Emails Using the Naive Bayes Classifier](07.02-Classifying-Emails-Using-Naive-Bayes.ipynb) >"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Implementing Our First Bayesian Classifier\n",
    "\n",
    "In the previous chapter, we learned how to generate a number of Gaussian blobs using\n",
    "scikit-learn. Do you remember how that is done?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating a toy dataset\n",
    "\n",
    "The function I'm referring to resides within scikit-learn's `datasets` module. Let's create 100\n",
    "data points, each belonging to one of two possible classes, and group them into two\n",
    "Gaussian blobs. To make the experiment reproducible, we specify an integer to pick a seed\n",
    "for the `random_state`. You can again pick whatever number you prefer. Here I went with\n",
    "Thomas Bayes' year of birth (just for kicks):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "X, y = datasets.make_blobs(100, 2, centers=2, random_state=1701, cluster_std=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's have a look at the dataset we just created using our trusty friend, Matplotlib:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('ggplot')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'm sure this is getting easier every time. We use scatter to create a scatter plot of all $x$\n",
    "values (`X[:, 0]`) and $y$ values (`X[:, 1]`), which will result in the following output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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TEAQBFSdO2LyeLkloLi1VMswu809KQpCNo5bib7gBvg5cOB/Wbsq8vcQZM+DlxhsumHAR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\nwiUiIiISZv8P+STeEAemaqMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c8bbc9f5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In agreement with our specifications, we see two different point clusters. They hardly\n",
    "overlap, so it should be relatively easy to classify them. What do you think—could a linear\n",
    "classifier do the job?\n",
    "\n",
    "Yes, it could. Recall that a linear classifier would try to draw a straight line through the\n",
    "figure, trying to put all blue dots on one side and all red dots on the other. A diagonal line\n",
    "going from the top-left corner to the bottom-right corner could clearly do the job. So we\n",
    "would expect the classification task to be relatively easy, even for a naive Bayes classifier.\n",
    "\n",
    "But first, don't forget to split the dataset into training and test sets! Here, I reserve 10% of\n",
    "the data points for testing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn import model_selection as ms\n",
    "X_train, X_test, y_train, y_test = ms.train_test_split(\n",
    "    X.astype(np.float32), y, test_size=0.1\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classifying the data with a normal Bayes classifier\n",
    "\n",
    "We will then use the same procedure as in earlier chapters to train a **normal Bayes\n",
    "classifier**. Wait, why not a naive Bayes classifier? Well, it turns out OpenCV doesn't really\n",
    "provide a true naive Bayes classifier... Instead, it comes with a Bayesian classifier that doesn't\n",
    "necessarily expect features to be independent, but rather expects the data to be clustered\n",
    "into Gaussian blobs. This is exactly the kind of dataset we created earlier!\n",
    "\n",
    "We can create a new classifier using the following function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import cv2\n",
    "model_norm = cv2.ml.NormalBayesClassifier_create()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, training is done via the `train` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_norm.train(X_train, cv2.ml.ROW_SAMPLE, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the classifier has been trained successfully, it will return True. We go through the\n",
    "motions of predicting and scoring the classifier, just like we have done a million times\n",
    "before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "_, y_pred = model_norm.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "metrics.accuracy_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even better—we can reuse the plotting function from the last chapter to inspect the decision\n",
    "boundary! If you recall, the idea was to create a mesh grid that would encompass all data\n",
    "points and then classify every point on the grid. The mesh grid is created via the NumPy\n",
    "function of the same name:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def plot_decision_boundary(model, X_test, y_test):\n",
    "    # create a mesh to plot in\n",
    "    h = 0.02  # step size in mesh\n",
    "    x_min, x_max = X_test[:, 0].min() - 1, X_test[:, 0].max() + 1\n",
    "    y_min, y_max = X_test[:, 1].min() - 1, X_test[:, 1].max() + 1\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                         np.arange(y_min, y_max, h))\n",
    "    \n",
    "    X_hypo = np.column_stack((xx.ravel().astype(np.float32),\n",
    "                              yy.ravel().astype(np.float32)))\n",
    "    ret = model.predict(X_hypo)\n",
    "    if isinstance(ret, tuple):\n",
    "        zz = ret[1]\n",
    "    else:\n",
    "        zz = ret\n",
    "    zz = zz.reshape(xx.shape)\n",
    "    \n",
    "    plt.contourf(xx, yy, zz, cmap=plt.cm.coolwarm, alpha=0.8)\n",
    "    plt.scatter(X_test[:, 0], X_test[:, 1], c=y_test, s=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Z/u7b6KuX1/ueMnocX9x6u6l6Uxe/8xbKGpMJ1l7+7tji++LuGUdRbh75W1Nx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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c8bd397630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plot_decision_boundary(model_norm, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So far, so good. The interesting part is that a Bayesian classifier also returns the probability\n",
    "with which each data point has been classified:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "ret, y_pred, y_proba = model_norm.predictProb(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function returns a Boolean flag (True for success, False for failure), the predicted\n",
    "target labels (`y_pred`), and the conditional probabilities (`y_proba`). Here, y_proba is an $N\n",
    "\\times 2$ matrix that indicates, for every one of the $N$ data points, the probability with which it\n",
    "was classified as either class 0 or class 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.16      ,  0.        ],\n",
       "       [ 0.        ,  0.28999999],\n",
       "       [ 0.19      ,  0.        ],\n",
       "       [ 0.23      ,  0.02      ],\n",
       "       [ 0.        ,  0.27000001],\n",
       "       [ 0.        ,  1.88      ],\n",
       "       [ 0.        ,  0.        ],\n",
       "       [ 0.        ,  1.88      ],\n",
       "       [ 0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ]], dtype=float32)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_proba.round(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classifying the data with a naive Bayes classifier\n",
    "\n",
    "We can compare the result to a true naïve Bayes classifier by asking scikit-learn for help:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn import naive_bayes\n",
    "model_naive = naive_bayes.GaussianNB()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As usual, training the classifier is done via the `fit` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GaussianNB(priors=None)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_naive.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scoring the classifier is built in:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_naive.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again a perfect score! However, in contrast to OpenCV, this classifier's `predict_proba`\n",
    "method returns true probability values, because all values are between 0 and 1, and because\n",
    "all rows add up to 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.],\n",
       "       [ 0.,  1.],\n",
       "       [ 0.,  1.],\n",
       "       [ 0.,  1.],\n",
       "       [ 1.,  0.],\n",
       "       [ 0.,  1.],\n",
       "       [ 1.,  0.],\n",
       "       [ 1.,  0.],\n",
       "       [ 0.,  1.],\n",
       "       [ 1.,  0.]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yprob = model_naive.predict_proba(X_test)\n",
    "yprob.round(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You might have noticed something else: This classifier has absolutely no doubt about the\n",
    "target label of each and every data point. It's all or nothing.\n",
    "\n",
    "The decision boundary returned by the naive Bayes classifier looks slightly different, but\n",
    "can be considered identical to the previous command for the purpose of this exercise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GsXfzVjb95R4c5b/U44oeM4YRl15KoAZ62uZ2vrM4HlInSwgvkvpZ4ihNwzJwMNqI0ViG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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c8bd513be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plot_decision_boundary(model_naive, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing conditional probabilities\n",
    "\n",
    "Similarly, we can also visualize probabilities. For this, we slightly modify the plot function\n",
    "from the previous example. We start out by creating a mesh grid between (`x_min`, `x_max`)\n",
    "and (`y_min`, `y_max`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def plot_proba(model, X_test, y_test):\n",
    "    # create a mesh to plot in\n",
    "    h = 0.02  # step size in mesh\n",
    "    x_min, x_max = X_test[:, 0].min() - 1, X_test[:, 0].max() + 1\n",
    "    y_min, y_max = X_test[:, 1].min() - 1, X_test[:, 1].max() + 1\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                         np.arange(y_min, y_max, h))\n",
    "    \n",
    "    X_hypo = np.column_stack((xx.ravel().astype(np.float32),\n",
    "                              yy.ravel().astype(np.float32)))\n",
    "    if hasattr(model, 'predictProb'):\n",
    "        _, _, y_proba = model.predictProb(X_hypo)\n",
    "    else:\n",
    "        y_proba = model.predict_proba(X_hypo)\n",
    "    \n",
    "    zz = y_proba[:, 1] - y_proba[:, 0]\n",
    "    zz = zz.reshape(xx.shape)\n",
    "    \n",
    "    plt.contourf(xx, yy, zz, cmap=plt.cm.coolwarm, alpha=0.8)\n",
    "    plt.scatter(X_test[:, 0], X_test[:, 1], c=y_test, s=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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31hmzTF3fLzwePGnrmXv3XdhCQhhy3nk+pyiBgUy//352vf5662OCghh/7bW4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\nt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3hcnP/Vo7j3wbPZsMtHtz/ycW/dXfbnzwSD0ONP3skLIpK4EilsxVvyNktITLy71c2N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\nEXGAQpaIiIiIAxSyRERERBzw/xe8bbFQxddqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c8bd42f908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plot_proba(model_naive, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<!--NAVIGATION-->\n",
    "< [Implementing a Spam Filter with Bayesian Learning](07.00-Implementing-a-Spam-Filter-with-Bayesian-Learning.ipynb) | [Contents](../README.md) | [Classifying Emails Using the Naive Bayes Classifier](07.02-Classifying-Emails-Using-Naive-Bayes.ipynb) >"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
